Shock Waves in Biological Tissues Under Telegraph Equation Heat Conduction

Heat conduction in live tissue during radiofrequency electrosurgery

“…Then, the non-dimensionalized problem to solve isnormal∂Tnormal∂t+∂2Tnormal∂t2=∂2Tnormal∂r2+2rnormal∂Tnormal∂ron the domain [0, 8] discretized into 400 segments with Δ r = 0.02. The initial and boundary conditions areTfalse(r,t=0false)=0,Tfalse(r=normalΔr,tfalse)=sin⁡(ωt)and2em2em2em2emTfalse(r=8,tfalse)=0.We then use a numerical method similar to the one described in [45] with second-order central differencing in space and the classic Runge–Kutta with Δ t = 0.006 in time to perform the simulation.…”

“…We set the relaxation time, conductivity, density and specific heat all equal to unity. Then, the non-dimensionalized problem to solve is We then use a numerical method similar to the one described in [45] with second-order central differencing in space and the classic Runge-Kutta with Δt = 0.006 in time to perform the simulation. Using a method similar to the one in [25], we measure the times t 1 and t 2 when the 'heat wave' reaches the locations r 1 and r 2 , so the phase velocity can be simply calculated as V p = (r 2 − r 1 )/(t 2 − t 1 ).…”